Lecture 24

class: center, middle, inverse, title-slide

.title[
# Lecture 24
]
.subtitle[
## MLR with Categorical Variables: Interactions
]
.author[
### Psych 10 C
]
.institute[
### University of California, Irvine
]
.date[
### 05/25/2022
]

---

## Model comparison: Simple linear regression models

- Last class we looked at the predictions of each of the following models:

- Null: `$$\text{Correct}_i \sim \text{Normal}(\beta_0, \sigma_1^2)$$`

- Age: `$$\text{Correct}_i \sim \text{Normal}(\beta_0+\beta_1\text{age-group}_i, \sigma_2^2)$$`

- Time: `$$\text{Correct}_i \sim \text{Normal}(\beta_0+\beta_2\text{time}_i, \sigma_3^2)$$`

---

## Model Comparison: Multiple linear regression models

- Age and Time additive: `$$\text{Correct}_i \sim \text{Normal}(\beta_0+\beta_1\text{age-group}_i+\beta_2\text{time}_i, \sigma_4^2)$$`

- Age and Time interaction:

`$$\text{Correct}_i \sim \text{Normal}(\beta_0+\beta_1\text{age-group}_i+\beta_2\text{time}_i+\beta_3\text{age-group}_i\text{time}_i, \sigma_5^2)$$`